Optimal Hedging under Price , Quantity and Exchange Rate Uncertainty

After devising expectational measures of production, price and exchange rate uncertainty, this paper presents a model to derive an optimal hedging strategy for a primary producer who is subject to variability on the price and the amount of its output and on the exchange rate risk when the final proceeds of its sales are not denominated in its currency of numeraire. In this model, it is assumed that the producer is a mean-variance maximizer. The analysis shows that the optimal hedge ratio for the commodity is proportional to the coefficient of the commodity futures prices bias in a linear regression where the producer's revenue uncertainty is the dependent variable. The ratios do not differ from the results that would have been obtained under price and quantity uncertainty only except when revenues are significantly correlated with the exchange rate variability. An empirical test of the model is carried out wherein cocoa is chosen as a case study. The countries selected in this test are three of the world's largest producers. Since their output is primarily sold on London markets, the dollar and the French franc have been empirically designated to hedge pound revenues. The ratio for cocoa is well below unity and ranges from 78 to 57 percent. For Ghana and the Ivory Coast, there is little correlation between revenue and exchange rate variability. Therefore, the cocoa ratio is not significantly affected by the introduction of this additional source of uncertainty and the currency ratio in the joint hedge is trivial for both the dollar and the franc. Nigeria's revenues, on the other hand, are correlated to the dollar and the cocoa ratio is de facto lowered by the currency effect in a joint cocoa-dollar hedge. Thesis Supervisor: John Parsons Title: Assistant Professor of Finance